Hi, we have a memory foam top on our mattress--not a soft pillow top, but the kind that kind of sinks in and conforms to your body. It's not firm, in other words, but it's not completely sink-down-into either. Would you let your baby sleep on a bed like this? This memory foam thing is huge and unweildy when not on the bed--not easily stored. I want to start sleeping with my son, but Im worried about SIDS. We have a spare room I can move to, which I think I might do, just to ease my mind. Just wanted to check with you guys too! Thank you for any response...